Journal of Optimization Theory and Applications

, Volume 11, Issue 5, pp 533–555

On the Stackelberg strategy in nonzero-sum games

  • M. Simaan
  • J. B. CruzJr.
Article

DOI: 10.1007/BF00935665

Cite this article as:
Simaan, M. & Cruz, J.B. J Optim Theory Appl (1973) 11: 533. doi:10.1007/BF00935665

Abstract

The properties of the Stackelberg solution in static and dynamic nonzero-sum two-player games are investigated, and necessary and sufficient conditions for its existence are derived. Several game problems, such as games where one of the two players does not know the other's performance criterion or games with different speeds in computing the strategies, are best modeled and solved within this solution concept. In the case of dynamic games, linear-quadratic problems are formulated and solved in a Hilbert space setting. As a special case, nonzero-sum linear-quadratic differential games are treated in detail, and the open-loop Stackelberg solution is obtained in terms of Riccati-like matrix differential equations. The results are applied to a simple nonzero-sum pursuit-evasion problem.

Copyright information

© Plenum Publishing Corporation 1973

Authors and Affiliations

  • M. Simaan
    • 1
  • J. B. CruzJr.
    • 1
  1. 1.Coordinated Science Laboratory and Department of Electrical EngineeringUniversity of IllinoisUrbana